Question

A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150- 0.01 x Demand for an annual printing of this particular product. The fixed costs per year (i.E., per printing) =$50,000 and the variable cost per unit =$40. What is the maximum profit that can be achieved if the maximum expected demand is 6,000 units per year? What is the unit price at this oint of optimal demand?

Answer 1

Answer:

a. The maximum profit that can be achieved is $300,000.

b. The unit price at this point of optimal demand is $90.

Explanation:

From the question, we can obtain the following:

x = Maximum expected demand = 6,000 units

Price = 150 - 0.01 x = 150 - (0.01 * 6,000) = 150 - 60 = $90

Fixed cost per year = $50,000

Variable cost per unit = $40

Total variable cost = Variable cost per unit * Maximum expected demand = $40 * 6,000 = $240,000

Total cost = Fixed cost + Total variable cost = $50,000 + $240,000 = $290,000

Revenue = Price * Maximum expected demand = $90 * 6,000 = $540,000

Therefore, we have:

a. What is the maximum profit that can be achieved if the maximum expected demand is 6,000 units per year?

Profit = Revenue - Total cost = $540,000 - $240,000 = $300,000

Therefore, the maximum profit that can be achieved is $300,000.

b. What is the unit price at this point of optimal demand?

As already stated above, the following are given in the question:

x = Maximum expected demand = 6,000

Price = 150 - 0.01 x ........................... (1)

Substitute for x in equation (1), we have:

Price = 150 - (0.01 * 6,000) = 150 - 60 = $90

Therefore, the unit price at this point of optimal demand is $90.